Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908726253846528 |
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| author | Uttenthal, Peter Vang |
| author_facet | Uttenthal, Peter Vang |
| contents | The distribution of primes raising the level of even Galois representations of tetrahedral type is studied. Data are presented on primes $v\leq 10^8$ raising the level of $3$-adic even representations of various conductors. Based on the data, a conjecture is formulated concerning the distribution of certain lines in the plane. By an application of Wiles' formula, the conjecture is shown to imply that the density of primes raising the level of a $p$-adic even representation is $$\frac{p-1}{p},$$ in agreement with the density of $2/3$ for $p=3$ observed in the data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14352 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane Uttenthal, Peter Vang Number Theory The distribution of primes raising the level of even Galois representations of tetrahedral type is studied. Data are presented on primes $v\leq 10^8$ raising the level of $3$-adic even representations of various conductors. Based on the data, a conjecture is formulated concerning the distribution of certain lines in the plane. By an application of Wiles' formula, the conjecture is shown to imply that the density of primes raising the level of a $p$-adic even representation is $$\frac{p-1}{p},$$ in agreement with the density of $2/3$ for $p=3$ observed in the data. |
| title | Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane |
| topic | Number Theory |
| url | https://arxiv.org/abs/2310.14352 |